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Exploring Phononic Properties of Two-Dimensional Materials using Machine Learning Interatomic Potentials
Bohayra Mortazavi, Ivan S. Novikov, Evgeny V. Podryabinkin, Stephan Roche, Timon Rabczuk, Alexander V. Shapeev, Xiaoying Zhuang
TL;DR
DFT accurately estimates phononic properties but becomes computationally demanding for low-symmetry and nanoporous structures, while computational setups can produce nonphysical imaginary frequencies. The paper uses machine-learning interatomic potentials passively trained on short ab-initio molecular dynamics trajectories, finding close agreement with DFT-based phononic and thermal-property results across diverse 2D materials. The method is presented as a stable and efficient approach for exploring complex 2D structures.
Problem
DFT-based phonon and thermal-property calculations become computationally demanding for low-symmetry and nanoporous structures, and setups may yield nonphysical imaginary frequencies.
Method
The study passively trains moment tensor potentials on short ab-initio molecular dynamics trajectories and uses them to replace DFT force calculations in phononic-property evaluations.
Results
Across diverse 2D lattices, MTPs closely reproduce DFPT phonon dispersions, group velocities, free energies, heat capacities, and entropies.
Takeaways & Limitations
The MTP-based approach offers an accurate, stable, and computationally efficient alternative for exploring phononic properties of low-symmetry and porous 2D materials.
Takeaways & Limitations
Some monoelemental structures show MTP inaccuracies, including poorly reproduced highest-frequency graphene optical modes and a spurious phagraphene soft mode.
Abstract
from arXiv · showhide
Phononic properties are commonly studied by calculating force constants using the density functional theory (DFT) simulations. Although DFT simulations offer accurate estimations of phonon dispersion relations or thermal properties, but for low-symmetry and nanoporous structures the computational cost quickly becomes very demanding. Moreover, the computational setups may yield nonphysical imaginary frequencies in the phonon dispersion curves, impeding the assessment of phononic properties and the dynamical stability of the considered system. Here, we compute phonon dispersion relations and examine the dynamical stability of a large ensemble of novel materials and compositions. We propose a fast and convenient alternative to DFT simulations which derived from machine-learning interatomic potentials passively trained over computationally efficient ab-initio molecular dynamics trajectories. Our results for diverse two-dimensional (2D) nanomaterials confirm that the proposed computational strategy can reproduce fundamental thermal properties in close agreement with those obtained via the DFT approach. The presented method offers a stable, efficient, and convenient solution for the examination of dynamical stability and exploring the phononic properties of low-symmetry and porous 2D materials.
1. Introduction
Phonon dispersion relations support analysis of crystal vibrations, transport properties, and dynamical stability. The paper motivates machine-learning interatomic potentials as an efficient alternative for complex 2D materials where DFT becomes demanding.
- Phonon dispersion relations characterize lattice dynamics and atomic vibrations in crystals.They also provide information about transport properties such as thermal conductivity and help examine dynamical stability.
- DFT commonly obtains phonon dispersion relations by calculating force constants and assesses thermal properties using supercell structures.DFT is computationally efficient for most highly symmetrical lattices but becomes demanding for low-symmetry and nanoporous structures.
- Passively trained moment tensor potentials use short, inexpensive ab-initio molecular dynamics trajectories to reproduce phononic properties for diverse 2D materials.The approach is presented as a stable and computationally efficient alternative for low-symmetry and nanoporous structures.
2. Computational methods
The computational workflow combines DFT and AIMD reference calculations with moment tensor potentials, which replace VASP force evaluations in PHONOPY-based phonon calculations. The method uses weighted training over energies, forces, and stresses and supports phononic-property evaluation for complex structures.
- Reference calculations: DFT calculations use VASP with PBE-GGA, specified plane-wave cutoffs, convergence tolerances, and 3×3×1 k-point grids.PHONOPY generates atomic displacements and obtains phonon dispersions and group velocities from DFPT inputs.
- MTP training: Moment tensor potentials describe interatomic interactions using parameters trained against energies, atomic forces, and stresses.The reported weights for energies, forces, and stresses are 1, 0.1, and 0.001, respectively.
- MTP representation: MTP basis functions are constructed from contractions of moment tensor descriptors and include radial and angular contributions.The radial contribution depends on interatomic distance and atom types, with smoothing near the cutoff radius.
- MTP training: Training an MTP requires solving a minimization problem over its potential parameters.The optimization weights express the relative importance of energies, forces, and stresses in the training objective.
- Phonon workflow: PHONOPY evaluates phononic properties with MTP replacing VASP during force calculations.The work provides training-set inputs, the MTP training procedure, and integration code for calculating MTP forces.
3. Results and discussions
Across monoelemental, binary, and ternary 2D lattices, passively trained MTPs closely reproduce DFT- or DFPT-based phononic properties while avoiding some nonphysical imaginary frequencies and reducing computational demands. Accuracy is generally high, though higher-temperature trajectories or larger AIMD supercells can improve optical-mode fidelity and stability.
- Monoelemental 2D lattices: MTPs closely reproduce phonon dispersion relations for diverse monoelemental 2D lattices, with inaccuracies concentrated in graphene’s highest-frequency optical modes and a phagraphene soft mode.The discrepancies are attributed to extrapolation from short, correlated 50 K AIMD training trajectories.
- Monoelemental 2D lattices: Higher-temperature AIMD trajectories remove the phagraphene imaginary frequencies and improve graphene’s high-frequency optical modes without affecting lower-frequency modes.The improvement preserves close agreement with DFPT at higher frequencies for phagraphene and improves graphene’s optical-mode accuracy.
- Binary 2D lattices: MTPs very accurately reproduce binary-lattice phonon dispersions, including acoustic modes, while eliminating slight Γ-point imaginary frequencies present in some DFPT results.The C3N4 monolayer’s conspicuous imaginary frequencies are reproduced by MTP, whereas slight optical-mode deviations occur for some C2N and BC3 samples.
- Ternary 2D lattices: For six ternary lattices, MTPs reproduce DFPT phonon dispersions and imaginary frequencies, with accuracy remaining insensitive to element count and structural complexity in the studied cases.Most cases required no additional AIMD trajectories, although higher-temperature data are expected to improve accuracy and stability when needed.
- Thermal and transport properties: MTPs closely reproduce phonon group velocities and show excellent agreement with DFPT for free energy, heat capacity, and entropy.The group-velocity agreement is excellent for several samples and remains free of substantial inaccuracies even in the worst cases.
- Computational advantages: The MTP approach offers lower-cost, less parameter-sensitive phononic calculations for complex 2D lattices, with marginal supercell-size costs and smoother acoustic dispersions near Γ.Short AIMD trajectories are less expensive than trajectories commonly used for thermal-stability studies, which usually exceed 10 ps.